in a game of simplified football a touchdown results in 7 points and a field goal results in 3 point. what is the largest score for a team not possible?

Cannot be multiple of 7 or 3. How high do you want to go?

11. Proved because once u get 3 possible scores in a row, all higher scores are possible by adding 3 to a lower score

Scores not possible are:

1,2,4,5,8,11....and then what?
12 = 4 x 3
13 = 7+3+3
14= 7 x 2
and every number higher has to be possible because we have 12, 13, and 14 possible, and any higher number can be obtained by adding 3 to any of these 3.
So, 11 is the highest number that is not possible.

To determine the largest score for a team that is not possible in a game of simplified football, we need to understand how scoring in the game works. Let's break it down:

According to the given information, a touchdown results in 7 points, and a field goal results in 3 points. From this, we can deduce that any possible score for a team will be a combination of touchdowns and field goals.

The question asks for the largest score that is not possible. To solve this, we need to identify the scores that can be achieved by a combination of touchdowns and field goals and then determine the largest score that cannot be formed.

To find all the possible scores, we can start by listing the various combinations of touchdowns and field goals:

- 0 touchdowns and 0 field goals = 0 points
- 1 touchdown and 0 field goals = 7 points
- 0 touchdowns and 1 field goal = 3 points
- 1 touchdown and 1 field goal = 10 points (7 + 3)
- 2 touchdowns and 0 field goals = 14 points (7 + 7)
- 0 touchdowns and 2 field goals = 6 points (3 + 3)
- 1 touchdown and 2 field goals = 16 points (7 + 3 + 3)
- 2 touchdowns and 1 field goal = 17 points (7 + 7 + 3)
- 3 touchdowns and 0 field goals = 21 points (7 + 7 + 7)
- 0 touchdowns and 3 field goals = 9 points (3 + 3 + 3)
- ...

By examining this list, we can see that every score from 0 to 21 points is possible, as it can be achieved using combinations of touchdowns and field goals. However, after 21 points, no combination of touchdowns and field goals can form a higher score.

Therefore, the largest score that is not possible is 22 points.

To determine this, we analyzed the pattern and systematically generated the possible scores. In this case, no complex calculations or formulas were required, but rather a logical approach to understanding the scoring system and listing out the various combinations.